(* ::Package:: *)

(************************************************************************)
(* This file was generated automatically by the Mathematica front end.  *)
(* It contains Initialization cells from a Notebook file, which         *)
(* typically will have the same name as this file except ending in      *)
(* ".nb" instead of ".m".                                               *)
(*                                                                      *)
(* This file is intended to be loaded into the Mathematica kernel using *)
(* the package loading commands Get or Needs.  Doing so is equivalent   *)
(* to using the Evaluate Initialization Cells menu command in the front *)
(* end.                                                                 *)
(*                                                                      *)
(* DO NOT EDIT THIS FILE.  This entire file is regenerated              *)
(* automatically each time the parent Notebook file is saved in the     *)
(* Mathematica front end.  Any changes you make to this file will be    *)
(* overwritten.                                                         *)
(************************************************************************)



<<ACPackages`


(* ::Section:: *)
(*\:041f\:043e\:0441\:0442\:0440\:043e\:0435\:043d\:0438\:0435 \:0441\:0438\:0441\:0442\:0435\:043c\:044b \:0438 \:043c\:0430\:0442\:0440\:0438\:0446*)


(* ::Subsection:: *)
(*(\:041f\:043e\:043b\:0443\:0447\:0435\:043d\:0438\:0435 \:0443\:0440\:0430\:0432\:043d\:0435\:043d\:0438\:0439 \:0441\:043c.CurvSystCoor-pseudotor.nb)*)
(*\:041e\:043f\:0440\:0435\:0434\:0435\:043b\:0435\:043d\:0438\:0435 \:0441\:0438\:0441\:0442\:0435\:043c\:044b eqs\[Phi]r[\[Lambda]_,\[Omega]_,\[Kappa]_,m_,Re_]*)


(* ::Text::Closed:: *)
(*\:0440\:0430\:0437\:043b\:043e\:0436\:0435\:043d\:043d\:043e\:0435 \:043f\:043e \:043c\:043e\:0434\:0430\:043c (\:0441 1-\:0439 \:043d\:0435\:0432\:0435\:0440\:043d\:043e, \:0442.\:043a. \:043d\:0435\:0442 \:0437\:0430\:0446\:0435\:043f\:043b\:0435\:043d\:0438\:044f \:043c\:043e\:0434)*)


(* ::Input:: *)
(*eqs\[Phi]r[\[Lambda]_,\[Omega]_,\[Kappa]_,m_,Re_]:=Which[m==0,{Re \[Lambda] \[Rho] v\[Zeta][\[Rho]]-*)
(*\!\(\*SuperscriptBox["v\[Zeta]", "\[Prime]",*)
(*MultilineFunction->None]\)[\[Rho]]-\[Rho] *)
(*\!\(\*SuperscriptBox["v\[Zeta]", "\[Prime]\[Prime]",*)
(*MultilineFunction->None]\)[\[Rho]],(-1+Re \[Lambda] \[Rho]^2) *)
(*\!\(\*SuperscriptBox["\[Psi]", "\[Prime]",*)
(*MultilineFunction->None]\)[\[Rho]]+\[Rho] ((1+Re \[Lambda] \[Rho]^2) *)
(*\!\(\*SuperscriptBox["\[Psi]", "\[Prime]\[Prime]",*)
(*MultilineFunction->None]\)[\[Rho]]-\[Rho] (2 *)
(*\!\(\*SuperscriptBox["\[Psi]", *)
(*TagBox[*)
(*RowBox[{"(", "3", ")"}],*)
(*Derivative],*)
(*MultilineFunction->None]\)[\[Rho]]+\[Rho] *)
(*\!\(\*SuperscriptBox["\[Psi]", *)
(*TagBox[*)
(*RowBox[{"(", "4", ")"}],*)
(*Derivative],*)
(*MultilineFunction->None]\)[\[Rho]]))},*)
(*m==1,{(1+Re \[Lambda] \[Rho]^2) v\[Zeta][\[Rho]]+\[Rho] (\[ImaginaryI] G Re \[Rho] \[Psi][\[Rho]]/2-( *)
(*\!\(\*SuperscriptBox["v\[Zeta]", "\[Prime]",*)
(*MultilineFunction->None]\)[\[Rho]]+\[Rho] *)
(*\!\(\*SuperscriptBox["v\[Zeta]", "\[Prime]\[Prime]",*)
(*MultilineFunction->None]\)[\[Rho]])),(-3+Re \[Lambda] \[Rho]^2) \[Psi][\[Rho]]+\[Rho] ((3-Re \[Lambda] \[Rho]^2) *)
(*\!\(\*SuperscriptBox["\[Psi]", "\[Prime]",*)
(*MultilineFunction->None]\)[\[Rho]]+\[Rho] (-(3+Re \[Lambda] \[Rho]^2) *)
(*\!\(\*SuperscriptBox["\[Psi]", "\[Prime]\[Prime]",*)
(*MultilineFunction->None]\)[\[Rho]]+\[Rho] (2 *)
(*\!\(\*SuperscriptBox["\[Psi]", *)
(*TagBox[*)
(*RowBox[{"(", "3", ")"}],*)
(*Derivative],*)
(*MultilineFunction->None]\)[\[Rho]]+\[Rho] *)
(*\!\(\*SuperscriptBox["\[Psi]", *)
(*TagBox[*)
(*RowBox[{"(", "4", ")"}],*)
(*Derivative],*)
(*MultilineFunction->None]\)[\[Rho]])))},*)
(*True,{(m^2+Re \[Lambda] \[Rho]^2) v\[Zeta][\[Rho]]+\[Rho] (\[ImaginaryI] G m Re \[Rho] \[Psi][\[Rho]]/2-( *)
(*\!\(\*SuperscriptBox["v\[Zeta]", "\[Prime]",*)
(*MultilineFunction->None]\)[\[Rho]]+\[Rho] *)
(*\!\(\*SuperscriptBox["v\[Zeta]", "\[Prime]\[Prime]",*)
(*MultilineFunction->None]\)[\[Rho]])),(m^2 (-4+m^2+Re \[Lambda] \[Rho]^2) \[Psi][\[Rho]]+\[Rho] ((1+2 m^2-Re \[Lambda] \[Rho]^2) *)
(*\!\(\*SuperscriptBox["\[Psi]", "\[Prime]",*)
(*MultilineFunction->None]\)[\[Rho]]-\[Rho] ((1+2 m^2+Re \[Lambda] \[Rho]^2) *)
(*\!\(\*SuperscriptBox["\[Psi]", "\[Prime]\[Prime]",*)
(*MultilineFunction->None]\)[\[Rho]]-\[Rho] (2 *)
(*\!\(\*SuperscriptBox["\[Psi]", *)
(*TagBox[*)
(*RowBox[{"(", "3", ")"}],*)
(*Derivative],*)
(*MultilineFunction->None]\)[\[Rho]]+\[Rho] *)
(*\!\(\*SuperscriptBox["\[Psi]", *)
(*TagBox[*)
(*RowBox[{"(", "4", ")"}],*)
(*Derivative],*)
(*MultilineFunction->None]\)[\[Rho]]))))}];*)


(* ::Text::Closed:: *)
(*\:0442\:0435\:043a\:0443\:0449\:0435\:0435: \:0441\:0438\:0441\:0442\:0435\:043c\:0430 \:0434\:043b\:044f \[Psi] \:0438 v\[Zeta], \:043e\:0431\:0440\:0435\:0437\:0430\:043d\:043d\:0430\:044f \:0434\:043e \[Kappa]^1*)
(*(eqs\[Phi]r[\[Lambda],\[Omega],\[Kappa],G,Re])*)


nd2=1;


eqs\[Phi]r[\[Lambda]_,\[Omega]_,\[Kappa]_,G_,Rn_]:={1/(Re \[Rho]) \[Kappa] (1/2 G Re \[Rho]^2 Sin[\[Phi]] \[Psi][\[Rho],\[Phi]]-Sin[\[Phi]] 
\!\(\*SuperscriptBox["v\[Zeta]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+(G Re Rn (-1+\[Rho]^2) (G (4-23 \[Rho]^2+7 \[Rho]^4)+24 (1-5 \[Rho]^2) \[Omega]) Sin[\[Phi]] 
\!\(\*SuperscriptBox["v\[Zeta]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]])/4608-1/4 G Re (-1+\[Rho]^2) Cos[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-2 Re \[Omega] Cos[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+1/737280 G Re (138240 (-1+3 \[Rho]^2)+G^2 Rn^2 (19-120 \[Rho]^2+150 \[Rho]^4-70 \[Rho]^6+9 \[Rho]^8)-40 G Rn^2 (-3+18 \[Rho]^2-20 \[Rho]^4+7 \[Rho]^6) \[Omega]) Cos[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+\[Rho] Cos[\[Phi]] 
\!\(\*SuperscriptBox["v\[Zeta]", 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-(G Re Rn \[Rho] (-1+\[Rho]^2)^2 (G (-4+\[Rho]^2)-24 \[Omega]) Cos[\[Phi]] 
\!\(\*SuperscriptBox["v\[Zeta]", 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]])/4608-1/4 G Re \[Rho] (-1+\[Rho]^2) Sin[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-2 Re \[Rho] \[Omega] Sin[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+1/737280 G Re \[Rho] (-1+\[Rho]^2) (138240+G^2 Rn^2 (-19+21 \[Rho]^2-9 \[Rho]^4+\[Rho]^6)-40 G Rn^2 (3-3 \[Rho]^2+\[Rho]^4) \[Omega]) Sin[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]])+\[Kappa]^2 ((Cos[\[Phi]]^2 v\[Zeta][\[Rho],\[Phi]])/Re+(G Rn (-1+\[Rho]^2)^2 (G (-4+\[Rho]^2)-24 \[Omega]) Cos[\[Phi]]^2 v\[Zeta][\[Rho],\[Phi]])/4608+(Sin[\[Phi]]^2 v\[Zeta][\[Rho],\[Phi]])/Re+(G Rn (-1+\[Rho]^2) (G (4-23 \[Rho]^2+7 \[Rho]^4)+24 (1-5 \[Rho]^2) \[Omega]) Sin[\[Phi]]^2 v\[Zeta][\[Rho],\[Phi]])/4608+1/2 G \[Rho]^2 Cos[\[Phi]] Sin[\[Phi]] \[Psi][\[Rho],\[Phi]]-1/737280 G (-1+\[Rho]^2) (138240+G^2 Rn^2 (-19+21 \[Rho]^2-9 \[Rho]^4+\[Rho]^6)-40 G Rn^2 (3-3 \[Rho]^2+\[Rho]^4) \[Omega]) Cos[\[Phi]] Sin[\[Phi]] \[Psi][\[Rho],\[Phi]]+1/737280 G (138240 (-1+3 \[Rho]^2)+G^2 Rn^2 (19-120 \[Rho]^2+150 \[Rho]^4-70 \[Rho]^6+9 \[Rho]^8)-40 G Rn^2 (-3+18 \[Rho]^2-20 \[Rho]^4+7 \[Rho]^6) \[Omega]) Cos[\[Phi]] Sin[\[Phi]] \[Psi][\[Rho],\[Phi]]-(Cos[\[Phi]] Sin[\[Phi]] 
\!\(\*SuperscriptBox["v\[Zeta]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]])/Re-(G Rn (-1+\[Rho]^2)^2 (G (-4+\[Rho]^2)-24 \[Omega]) Cos[\[Phi]] Sin[\[Phi]] 
\!\(\*SuperscriptBox["v\[Zeta]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]])/4608+1/59454259200 G nd2 Rn (-1+\[Rho]^2) (G^3 Rn^2 (-4979+20521 \[Rho]^2-13499 \[Rho]^4+4421 \[Rho]^6-829 \[Rho]^8+35 \[Rho]^10)-193536000 (-1+3 \[Rho]^2) \[Omega]-16 G^2 Rn^2 (3111-11789 \[Rho]^2+5536 \[Rho]^4-1184 \[Rho]^6+216 \[Rho]^8) \[Omega]-6720 G (-10752+17 Rn^2 \[Omega]^2+5 Rn^2 \[Rho]^6 \[Omega]^2+\[Rho]^2 (38784-55 Rn^2 \[Omega]^2)+\[Rho]^4 (-13056+5 Rn^2 \[Omega]^2))) Sin[2 \[Phi]] 
\!\(\*SuperscriptBox["v\[Zeta]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-1/4 G (-1+\[Rho]^2) Cos[\[Phi]]^2 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-1/737280 G (-1+\[Rho]^2) (138240+G^2 Rn^2 (-19+21 \[Rho]^2-9 \[Rho]^4+\[Rho]^6)-40 G Rn^2 (3-3 \[Rho]^2+\[Rho]^4) \[Omega]) Cos[\[Phi]]^2 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+1/59929893273600 G nd2 (8820 (G^4 Rn^4 (-1+\[Rho]^2)^3 (76-103 \[Rho]^2+57 \[Rho]^4-13 \[Rho]^6+\[Rho]^8)+184320 G Rn^2 (-35+60 \[Rho]^2-30 \[Rho]^4+\[Rho]^6) \[Omega]-8 G^3 Rn^4 (-1+\[Rho]^2)^3 (-117+138 \[Rho]^2-62 \[Rho]^4+8 \[Rho]^6) \[Omega]-35389440 (42+Rn^2 \[Omega]^2+Rn^2 \[Rho]^4 \[Omega]^2-2 \[Rho]^2 (33+Rn^2 \[Omega]^2))+192 G^2 Rn^2 (5 Rn^2 \[Rho]^10 \[Omega]^2+\[Rho]^4 (2880-95 Rn^2 \[Omega]^2)+60 \[Rho]^2 (-28+Rn^2 \[Omega]^2)+15 \[Rho]^6 (-96+5 Rn^2 \[Omega]^2)-6 \[Rho]^8 (-28+5 Rn^2 \[Omega]^2)-3 (168+5 Rn^2 \[Omega]^2)))+(G^4 Rn^4 (-145690+771792 \[Rho]^2-1244565 \[Rho]^4+980784 \[Rho]^6-448350 \[Rho]^8+131544 \[Rho]^10-20727 \[Rho]^12+1280 \[Rho]^14)-325140480 G Rn^2 (-101+380 \[Rho]^2-330 \[Rho]^4+84 \[Rho]^6) \[Omega]-252 G^3 Rn^4 (6017-31504 \[Rho]^2+49530 \[Rho]^4-36960 \[Rho]^6+15050 \[Rho]^8-3552 \[Rho]^10+329 \[Rho]^12) \[Omega]+26011238400 (9 Rn^2 \[Rho]^4 \[Omega]^2+5 (-72+Rn^2 \[Omega]^2)-16 \[Rho]^2 (-45+Rn^2 \[Omega]^2))+4032 G^2 Rn^2 (777840-923 Rn^2 \[Omega]^2+288 Rn^2 \[Rho]^10 \[Omega]^2+5040 \[Rho]^6 (-448+Rn^2 \[Omega]^2)-1750 \[Rho]^8 (-192+Rn^2 \[Omega]^2)+280 \[Rho]^2 (-12912+17 Rn^2 \[Omega]^2)-315 \[Rho]^4 (-14544+23 Rn^2 \[Omega]^2))) Cos[2 \[Phi]]) 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+(\[Rho] Cos[\[Phi]]^2 
\!\(\*SuperscriptBox["v\[Zeta]", 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]])/Re-1/59454259200 G nd2 Rn \[Rho] (-1+\[Rho]^2)^2 (G^3 Rn^2 (4979-2792 \[Rho]^2+777 \[Rho]^4-134 \[Rho]^6+5 \[Rho]^8)-193536000 \[Omega]-16 G^2 Rn^2 (-3111+1228 \[Rho]^2-208 \[Rho]^4+36 \[Rho]^6) \[Omega]-6720 G (10752-17 Rn^2 \[Omega]^2+Rn^2 \[Rho]^4 \[Omega]^2+2 \[Rho]^2 (-1632+Rn^2 \[Omega]^2))) Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["v\[Zeta]", 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-(G Rn \[Rho] (-1+\[Rho]^2)^2 (G (-4+\[Rho]^2)-24 \[Omega]) Sin[\[Phi]]^2 
\!\(\*SuperscriptBox["v\[Zeta]", 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]])/4608-1/737280 G \[Rho] (-1+\[Rho]^2) (138240+G^2 Rn^2 (-19+21 \[Rho]^2-9 \[Rho]^4+\[Rho]^6)-40 G Rn^2 (3-3 \[Rho]^2+\[Rho]^4) \[Omega]) Cos[\[Phi]] Sin[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-1/8 G \[Rho] (-1+\[Rho]^2) Sin[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+1/59929893273600 G nd2 \[Rho] (-1+\[Rho]^2) (G^4 Rn^4 (145690-240206 \[Rho]^2+174649 \[Rho]^4-70547 \[Rho]^6+19123 \[Rho]^8-2801 \[Rho]^10+160 \[Rho]^12)-325140480 G Rn^2 (101-89 \[Rho]^2+21 \[Rho]^4) \[Omega]-252 G^3 Rn^4 (-6017+9735 \[Rho]^2-6775 \[Rho]^4+2465 \[Rho]^6-545 \[Rho]^8+47 \[Rho]^10) \[Omega]+26011238400 (360+Rn^2 (-5+3 \[Rho]^2) \[Omega]^2)+4032 G^2 Rn^2 (-777840+923 Rn^2 \[Omega]^2+48 Rn^2 \[Rho]^8 \[Omega]^2+\[Rho]^2 (1029840-1457 Rn^2 \[Omega]^2)+\[Rho]^6 (67200-302 Rn^2 \[Omega]^2)+\[Rho]^4 (-497280+958 Rn^2 \[Omega]^2))) Sin[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]])+1/(2 Re \[Rho]^2) (2 Re \[Lambda] \[Rho]^2 v\[Zeta][\[Rho],\[Phi]]+G Re \[Rho]^2 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-2 (
\!\(\*SuperscriptBox["v\[Zeta]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "2"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+\[Rho] (
\!\(\*SuperscriptBox["v\[Zeta]", 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+\[Rho] 
\!\(\*SuperscriptBox["v\[Zeta]", 
TagBox[
RowBox[{"(", 
RowBox[{"2", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]))),1/(Re \[Rho]^4) (4 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "2"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-Re \[Lambda] \[Rho]^2 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "2"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "4"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+\[Rho] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-Re \[Lambda] \[Rho]^3 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-2 \[Rho] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"1", ",", "2"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-\[Rho]^2 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"2", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-Re \[Lambda] \[Rho]^4 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"2", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+2 \[Rho]^2 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"2", ",", "2"}], ")"}],
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\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
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\!\(\*SuperscriptBox["v\[Zeta]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+72 G^2 Re Rn \[Rho]^2 Sin[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-4608 Re \[Lambda] \[Rho]^2 Sin[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-432 G^2 Re Rn \[Rho]^4 Sin[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+240 G^2 Re Rn \[Rho]^6 Sin[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+384 G Re Rn \[Rho]^2 \[Omega] Sin[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-1728 G Re Rn \[Rho]^4 \[Omega] Sin[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "1"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+18432 Cos[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "2"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+8 G^2 Re Rn Cos[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "2"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-18 G^2 Re Rn \[Rho]^2 Cos[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"0", ",", "2"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+12 G^2 Re Rn \[Rho]^4 Cos[\[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
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RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+4979 G^4 nd2 Re Rn^3 \[Rho]^3 Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+166440960 G^2 nd2 Re Rn \[Rho]^5 Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-12750 G^4 nd2 Re Rn^3 \[Rho]^5 Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-116121600 G^2 nd2 Re Rn \[Rho]^7 Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+11340 G^4 nd2 Re Rn^3 \[Rho]^7 Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+21934080 G^2 nd2 Re Rn \[Rho]^9 Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-4480 G^4 nd2 Re Rn^3 \[Rho]^9 Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+1050 G^4 nd2 Re Rn^3 \[Rho]^11 Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-144 G^4 nd2 Re Rn^3 \[Rho]^13 Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+5 G^4 nd2 Re Rn^3 \[Rho]^15 Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-193536000 G nd2 Re Rn \[Rho]^3 \[Omega] Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+49776 G^3 nd2 Re Rn^3 \[Rho]^3 \[Omega] Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+387072000 G nd2 Re Rn \[Rho]^5 \[Omega] Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-119200 G^3 nd2 Re Rn^3 \[Rho]^5 \[Omega] Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-193536000 G nd2 Re Rn \[Rho]^7 \[Omega] Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+92400 G^3 nd2 Re Rn^3 \[Rho]^7 \[Omega] Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-26880 G^3 nd2 Re Rn^3 \[Rho]^9 \[Omega] Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+4480 G^3 nd2 Re Rn^3 \[Rho]^11 \[Omega] Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-576 G^3 nd2 Re Rn^3 \[Rho]^13 \[Omega] Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+114240 G^2 nd2 Re Rn^3 \[Rho]^3 \[Omega]^2 Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-241920 G^2 nd2 Re Rn^3 \[Rho]^5 \[Omega]^2 Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+134400 G^2 nd2 Re Rn^3 \[Rho]^7 \[Omega]^2 Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-6720 G^2 nd2 Re Rn^3 \[Rho]^11 \[Omega]^2 Cos[2 \[Phi]] 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-51609600 G^2 Re Rn \[Rho]^3 Sin[\[Phi]]^2 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+116121600 G^2 Re Rn \[Rho]^5 Sin[\[Phi]]^2 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-77414400 G^2 Re Rn \[Rho]^7 Sin[\[Phi]]^2 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+12902400 G^2 Re Rn \[Rho]^9 Sin[\[Phi]]^2 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-309657600 G Re Rn \[Rho]^3 \[Omega] Sin[\[Phi]]^2 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]+619315200 G Re Rn \[Rho]^5 \[Omega] Sin[\[Phi]]^2 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]]-309657600 G Re Rn \[Rho]^7 \[Omega] Sin[\[Phi]]^2 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"3", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]])+\[Rho]^4 
\!\(\*SuperscriptBox["\[Psi]", 
TagBox[
RowBox[{"(", 
RowBox[{"4", ",", "0"}], ")"}],
Derivative],
MultilineFunction->None]\)[\[Rho],\[Phi]])};


(* ::Input:: *)
(*eqs\[Phi]r[\[Lambda],0,0,G,R]*)


(* ::Subsection:: *)
(*\:041f\:043e\:043b\:0443\:0447\:0435\:043d\:0438\:0435 \:0441\:0438\:0441\:0442\:0435\:043c\:044b \:0434\:043b\:044f \:043d\:0430\:0445\:043e\:0436\:0434\:0435\:043d\:0438\:044f \:0438\:043d\:043a\:0440\:0435\:043c\:0435\:043d\:0442\:043e\:0432*)


(* ::Subsubsection::Closed:: *)
(*\:041f\:043e\:043b\:0443\:0447\:0435\:043d\:0438\:0435 \:0431\:0430\:0437\:0438\:0441\:043d\:044b\:0445 \:0444\:0443\:043d\:043a\:0446\:0438\:0439 (\:043d\:0443\:043b\:0438 \:0411\:0435\:0441\:0441\:0435\:043b\:044f)*)


bz[i\[Phi]_,ir_]:=bz[i\[Phi],ir]=If[ir==0,0KroneckerDelta[ir,i\[Phi]],N[BesselJZero[i\[Phi],ir]]]


(* ::Text::Closed:: *)
(*\:041f\:0440\:043e\:0432\:0435\:0440\:043a\:0438*)


(* ::Input:: *)
(*Manipulate[Table[bz[i,j],{j,5}],{i,0,5,1}]*)


(* ::Input:: *)
(*Manipulate[N[Table[BesselJZero[i,j],{j,5}]],{i,0,5,1}]*)


(* ::Input:: *)
(*Manipulate[Plot[BesselJ[i\[Phi],bz[i\[Phi],ir]r],{r,0,1}],{i\[Phi],0,5,1},{ir,1,5,1}]*)


(* ::Subsubsection::Closed:: *)
(*\:0412\:044b\:0434\:0435\:043b\:0435\:043d\:0438\:0435 \:043a\:043e\:044d\:0444\:0444\:0438\:0446\:0438\:0435\:043d\:0442\:043e\:0432*)


(* ::Text::Closed:: *)
(*\:0423\:0441\:0442\:0430\:0440\:0435\:0432\:0448\:0438\:0435 \:0432\:0435\:0440\:0441\:0438\:0438 \:0444\:0443\:043d\:043a\:0446\:0438\:0439*)


(* ::Input:: *)
(*BesselNorm[i\[Phi]_,ir_]:=\!\( *)
(*\*UnderoverscriptBox[\(\[Integral]\), \(0\), \(1\)]r\ *)
(*SuperscriptBox[\(BesselJ[i\[Phi], bz[i\[Phi], ir] r]\), \(2\)] \[DifferentialD]r\)*)
(*(* (\:043d\:0435 \:043f\:0440\:0438\:043c\:0435\:043d\:044f\:0442\:044c \:0432 \:0441\:0438\:043c\:0432\:043e\:043b\:044c\:043d\:043e\:043c \:0432\:0438\:0434\:0435!bz \:0433\:043b\:044e\:0447\:0438\:0442) - \:0442\:043e \:0436\:0435 \:0441\:0430\:043c\:043e\:0435, \:043d\:043e \:0434\:043e\:043b\:044c\:0448\:0435*)*)


(* ::Input:: *)
(*BesselScalar[if1_,ir1_,if2_,ir2_]:=If[if1==if2,KroneckerDelta[ir1,ir2]BesselNorm[if1,ir1],NIntegrate[\[Rho] BesselJ[if1,bz[if1,ir1]\[Rho]]BesselJ[if2,bz[if2,ir2]\[Rho]],{\[Rho],0,1}]];*)


(* ::Input:: *)
(*(*n=i\[Phi],mun=Subscript[\[Mu], n]=ir*)*)
(*GetHarmCoef[expr_,i\[Phi]_,ir_]:=Block[{\[Rho],\[Phi]},1/(2\[Pi] BesselNorm[i\[Phi],ir]) \!\( *)
(*\*UnderoverscriptBox[\(\[Integral]\), \(0\), \(1\)]\( *)
(*\*UnderoverscriptBox[\(\[Integral]\), \(0\), \(2  \[Pi]\)]\[Rho]\ expr\ BesselJ[i\[Phi], bz[i\[Phi], ir]\ \[Rho]]\ *)
(*SuperscriptBox[\(E\), \(\(-\[ImaginaryI]\)\ i\[Phi]\ \[Phi]\)] \[DifferentialD]\[Phi] \[DifferentialD]\[Rho]\)\)]*)


(* ::Input:: *)
(*GetHarmCoef[expr_,i\[Phi]_,ir_]:=Block[{\[Rho],\[Phi]},1/(2\[Pi] BesselNorm[i\[Phi],ir]) NIntegrate[\[Rho] expr BesselJ[i\[Phi],bz[i\[Phi],ir] \[Rho]] E^(-\[ImaginaryI] i\[Phi] \[Phi]),{\[Phi],0,2\[Pi]},{\[Rho],0,1}]]*)


BesselNorm[i\[Phi]_,ir_]:=If[ir==0,KroneckerDelta[ir,i\[Phi]]/2,BesselJ[i\[Phi]+1,bz[i\[Phi],ir]]^2/2]


BesselScalar[weight_,if1_,ir1_,if2_,ir2_,rvar_]:=
BesselScalar[weight,if1,ir1,if2,ir2,rvar]=Block[{funcs=BesselJ[if1,bz[if1,ir1]rvar]BesselJ[if2,bz[if2,ir2]rvar],zerord},
(*Print["bs",{weight,if1,ir1,if2,ir2}];*)
zerord=Position[CoefficientList[Series[funcs,{\[Rho],0,Exponent[weight,rvar^-1]-1}],\[Rho]],_?(#!=0&)]-1;Return[If[Depth[zerord]==3,$Failed,If[if1==if2\[And]FreeQ[weight/\[Rho],\[Rho]],weight/\[Rho] KroneckerDelta[ir1,ir2]BesselNorm[if1,ir1],NIntegrate[Evaluate[weight funcs],{rvar,0,1}]]]];
];
BesselScalar[weight_,if1_,if1a_,ir1_,if2_,if2a_,ir2_,rvar_]:=
BesselScalar[weight,if1,if1a,ir1,if2,if2a,ir2,rvar]=Block[{funcs=BesselJ[if1,bz[if1a,ir1]rvar]BesselJ[if2,bz[if2a,ir2]rvar],zerord},
(*Print["bs",{weight,if1,if1a,ir1,if2,if2a,ir2}];*)
zerord=Position[CoefficientList[Series[funcs,{\[Rho],0,Exponent[weight,rvar^-1]-1}],\[Rho]],_?(#!=0&)]-1;
Return[If[Depth[zerord]==3,$Failed,If[if1==if2==if1a==if2a\[And]FreeQ[weight/\[Rho],\[Rho]],weight/\[Rho] KroneckerDelta[ir1,ir2]BesselNorm[if1,ir1],NIntegrate[Evaluate[weight funcs],{rvar,0,1}]]]];
];


(* ::Text:: *)
(*n=i\[Phi],mun=Subscript[\[Mu], n]=ir*)


(* ::Text::Closed:: *)
(*\:041f\:043e\:0434\:0441\:0442\:0430\:043d\:043e\:0432\:043a\:0438 \:0434\:043b\:044f \:0432\:044b\:043f\:043e\:043b\:043d\:0435\:043d\:0438\:044f \:0440\:0443\:0447\:043d\:043e\:0433\:043e \:0438\:043d\:0442\:0435\:0433\:0440\:0438\:0440\:043e\:0432\:0430\:043d\:0438\:044f \:043f\:043e \[Phi] (\:0438\:0441\:043f\:043e\:043b\:044c\:0437\:0443\:044e\:0442\:0441\:044f \:0432 \:0444\:0443\:043d\:043a\:0446\:0438\:044f\:0445 GetCoef/Symb).*)
(*\:041e\:0441\:0442\:043e\:0440\:043e\:0436\:043d\:043e! \:041d\:0435 \:0440\:0430\:0431\:043e\:0442\:0430\:0435\:0442 \:0441 \:0432\:044b\:0440\:0430\:0436\:0435\:043d\:0438\:044f\:043c\:0438 \:0442\:0438\:043f\:0430 E^(-2\[ImaginaryI]  \[Phi]) Sin[\[Phi]]Cos[\[Phi]]*)


(* ::Input:: *)
(*\[Phi]integr={a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Sin[\[Phi] n_.]/;n^2!=m^2:>a (-n+\[ExponentialE]^(2 \[ImaginaryI] m \[Pi]) (n Cos[2 n \[Pi]]-\[ImaginaryI] m Sin[2 n \[Pi]]))/(2 (m-n) (m+n) \[Pi]),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Cos[\[Phi] n_.]/;n^2!=m^2:>a (\[ImaginaryI] (m+\[ExponentialE]^(2 \[ImaginaryI] m \[Pi]) (-m Cos[2 n \[Pi]]+\[ImaginaryI] n Sin[2 n \[Pi]])))/(2 (m-n) (m+n) \[Pi]),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Sin[\[Phi] n_.]/;n==m&&n!=0:>a (1-\[ExponentialE]^(4 \[ImaginaryI] n \[Pi])+4 \[ImaginaryI] n \[Pi])/(8 n \[Pi]),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Cos[\[Phi] n_.]/;n==m&&n!=0:>a (\[ImaginaryI]-\[ImaginaryI] \[ExponentialE]^(4 \[ImaginaryI] n \[Pi])+4 n \[Pi])/(8 n \[Pi]),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Sin[\[Phi] n_.]/;n==-m&&n!=0:>a (-1+\[ExponentialE]^(4 \[ImaginaryI] m \[Pi])-4 \[ImaginaryI] m \[Pi])/(8 m \[Pi]),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Cos[\[Phi] n_.]/;n==-m&&n!=0:>a (\[ImaginaryI]-\[ImaginaryI] \[ExponentialE]^(4 \[ImaginaryI] m \[Pi])+4 m \[Pi])/(8 m \[Pi]),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]):>a (\[ImaginaryI] (m-\[ExponentialE]^(2 \[ImaginaryI] m \[Pi]) m))/(2 m^2 \[Pi]),a_. Sin[\[Phi] n_.]/;n!=0:>-a(-n+n Cos[2 n \[Pi]])/(2 n^2 \[Pi]),a_. Cos[\[Phi] n_.]/;n!=0:>a Sin[2 n \[Pi]]/(2 n \[Pi])};*)


(* ::Input:: *)
(*\[Phi]integrdebug={a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Sin[\[Phi] n_.]/;n^2!=m^2:>(Print[{1,n,m}];a (-n+\[ExponentialE]^(2 \[ImaginaryI] m \[Pi]) (n Cos[2 n \[Pi]]-\[ImaginaryI] m Sin[2 n \[Pi]]))/(2 (m-n) (m+n) \[Pi])),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Cos[\[Phi] n_.]/;n^2!=m^2:>(Print[{2,n,m}];a (\[ImaginaryI] (m+\[ExponentialE]^(2 \[ImaginaryI] m \[Pi]) (-m Cos[2 n \[Pi]]+\[ImaginaryI] n Sin[2 n \[Pi]])))/(2 (m-n) (m+n) \[Pi])),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Sin[\[Phi] n_.]/;n==m&&n!=0:>(Print[{3,n,m}];a (1-\[ExponentialE]^(4 \[ImaginaryI] n \[Pi])+4 \[ImaginaryI] n \[Pi])/(8 n \[Pi])),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Cos[\[Phi] n_.]/;n==m&&n!=0:>(Print[{4,n,m}];a (\[ImaginaryI]-\[ImaginaryI] \[ExponentialE]^(4 \[ImaginaryI] n \[Pi])+4 n \[Pi])/(8 n \[Pi])),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Sin[\[Phi] n_.]/;n==-m&&n!=0:>(Print[{5,n,m}];a (-1+\[ExponentialE]^(4 \[ImaginaryI] m \[Pi])-4 \[ImaginaryI] m \[Pi])/(8 m \[Pi])),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Cos[\[Phi] n_.]/;n==-m&&n!=0:>(Print[{6,n,m}];a (\[ImaginaryI]-\[ImaginaryI] \[ExponentialE]^(4 \[ImaginaryI] m \[Pi])+4 m \[Pi])/(8 m \[Pi])),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]):>(Print[{7,n,m}];a (\[ImaginaryI] (m-\[ExponentialE]^(2 \[ImaginaryI] m \[Pi]) m))/(2 m^2 \[Pi])),a_. Sin[\[Phi] n_.]/;n!=0:>(Print[{8,n,m}];-a(-n+n Cos[2 n \[Pi]])/(2 n^2 \[Pi])),a_. Cos[\[Phi] n_.]/;n!=0:>(Print[{9,n,m}];a Sin[2 n \[Pi]]/(2 n \[Pi]))};*)


GetHarmCoef[expr_,i\[Phi]_,ir_]:=Block[{\[Rho],\[Phi],vir,opts,eps=0 10^-6},
Off[NIntegrate::"ploss"];
vir=Chop[1/(2\[Pi]) \!\(
\*UnderoverscriptBox[\(\[Integral]\), \(0\), \(2  \[Pi]\)]Expand[expr]\ 
SuperscriptBox[\(E\), \(\(-\[ImaginaryI]\)\ i\[Phi]\ \[Phi]\)] \[DifferentialD]\[Phi]\)];
(*\[Phi]integr=...;vir=Chop[Expand[expr E^(-\[ImaginaryI] i\[Phi] \[Phi])]/.\[Phi]integr];*)
opts=Sequence[MaxRecursion->20];
Return[Expand[1/BesselNorm[i\[Phi],ir] vir BesselJ[i\[Phi],bz[i\[Phi],ir]\[Rho]]\[Rho]]/.{BesselJ[i1_,k1_ \[Rho]]BesselJ[i2_,k2_ \[Rho]]\[Rho]^por_.:>NIntegrate[BesselJ[i1,k1 \[Rho]]BesselJ[i2,k2 \[Rho]]\[Rho]^por,{\[Rho],eps,1},Evaluate[opts]],BesselJ[i1_,k1_ \[Rho]]BesselJ[i2_,k2_ \[Rho]]:>NIntegrate[BesselJ[i1,k1 \[Rho]]BesselJ[i2,k2 \[Rho]],{\[Rho],eps,1},Evaluate[opts]],BesselJ[i1_,k1_ \[Rho]]^2 \[Rho]^por_.:>NIntegrate[BesselJ[i1,k1 \[Rho]]^2 \[Rho]^por,{\[Rho],eps,1},Evaluate[opts]],BesselJ[i1_,k1_ \[Rho]]^2:>NIntegrate[BesselJ[i1,k1 \[Rho]]^2,{\[Rho],eps,1},Evaluate[opts]],a_. BesselJ[i1_,k1_ \[Rho]]:>NIntegrate[a BesselJ[i1,k1 \[Rho]],{\[Rho],eps,1},Evaluate[opts]]}];
On[NIntegrate::"ploss"];
];


{ts\[Phi],ts1,ts2,tsoth,tslast}={0,0,0,0,0};


(* ::Input:: *)
(*{ts\[Phi],ts1,ts2,tsoth,tslast}*)


GetHarmCoefSymb[expr_,i\[Phi]_,ir_]:=Block[{\[Rho],\[Phi],vir,opts,temp,a,b,\[Phi]integr},
Off[NIntegrate::"ploss"];
\[Phi]integr={a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Sin[\[Phi] n_.]/;n^2!=m^2:>a (-n+\[ExponentialE]^(2 \[ImaginaryI] m \[Pi]) (n Cos[2 n \[Pi]]-\[ImaginaryI] m Sin[2 n \[Pi]]))/(2 (m-n) (m+n) \[Pi]),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Cos[\[Phi] n_.]/;n^2!=m^2:>a (\[ImaginaryI] (m+\[ExponentialE]^(2 \[ImaginaryI] m \[Pi]) (-m Cos[2 n \[Pi]]+\[ImaginaryI] n Sin[2 n \[Pi]])))/(2 (m-n) (m+n) \[Pi]),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Sin[\[Phi] n_.]/;n==m&&n!=0:>a (1-\[ExponentialE]^(4 \[ImaginaryI] n \[Pi])+4 \[ImaginaryI] n \[Pi])/(8 n \[Pi]),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Cos[\[Phi] n_.]/;n==m&&n!=0:>a (\[ImaginaryI]-\[ImaginaryI] \[ExponentialE]^(4 \[ImaginaryI] n \[Pi])+4 n \[Pi])/(8 n \[Pi]),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Sin[\[Phi] n_.]/;n==-m&&n!=0:>a (-1+\[ExponentialE]^(4 \[ImaginaryI] m \[Pi])-4 \[ImaginaryI] m \[Pi])/(8 m \[Pi]),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]) Cos[\[Phi] n_.]/;n==-m&&n!=0:>a (\[ImaginaryI]-\[ImaginaryI] \[ExponentialE]^(4 \[ImaginaryI] m \[Pi])+4 m \[Pi])/(8 m \[Pi]),a_. \[ExponentialE]^(\[Phi] Complex[0,m_]):>a (\[ImaginaryI] (m-\[ExponentialE]^(2 \[ImaginaryI] m \[Pi]) m))/(2 m^2 \[Pi]),a_. Sin[\[Phi] n_.]/;n!=0:>-a(-n+n Cos[2 n \[Pi]])/(2 n^2 \[Pi]),a_. Cos[\[Phi] n_.]/;n!=0:>a Sin[2 n \[Pi]]/(2 n \[Pi])};(*ts\[Phi]+=First[Timing[vir=Chop[1/(2\[Pi] )\!\(
\*UnderoverscriptBox[\(\[Integral]\), \(0\), \(2  \[Pi]\)]Expand[expr]\ 
SuperscriptBox[\(E\), \(\(-\[ImaginaryI]\)\ i\[Phi]\ \[Phi]\)] \[DifferentialD]\[Phi]\)];]];*)
ts\[Phi]+=First[Timing[vir=Chop[TrigReduce[Expand[expr E^(-\[ImaginaryI] i\[Phi] \[Phi])]]/.\[Phi]integr];]];
(*opts=Sequence[MaxRecursion->20];*)
temp=Expand[1/BesselNorm[i\[Phi],ir] vir BesselJ[i\[Phi],\[Beta][i\[Phi],ir]\[Rho]]\[Rho]]+Pif;
ts1+=First[Timing[temp=Replace[temp,{b_. BesselJ[i1_,\[Beta][i1_,k1_]\[Rho]]BesselJ[i2_,\[Beta][i2_,k2_]\[Rho]]\[Rho]^a_./;BesselScalar[\[Rho]^a,i1,k1,i2,k2,\[Rho]]=!=$Failed\[And]FreeQ[b,\[Rho]]:>b BesselScalar[\[Rho]^a,i1,k1,i2,k2,\[Rho]],b_. BesselJ[i1_,\[Beta][i1_,k1_]\[Rho]]BesselJ[i2_,\[Beta][i2_,k2_]\[Rho]]/;BesselScalar[1,i1,k1,i2,k2,\[Rho]]=!=$Failed\[And]FreeQ[b,\[Rho]]:>b BesselScalar[1,i1,k1,i2,k2,\[Rho]],b_. BesselJ[i1_,\[Beta][i1_,k1_]\[Rho]]^2 \[Rho]^a_./;BesselScalar[\[Rho]^a,i1,k1,i1,k1,\[Rho]]=!=$Failed\[And]FreeQ[b,\[Rho]]:>b BesselScalar[\[Rho]^a,i1,k1,i1,k1,\[Rho]],b_. BesselJ[i1_,\[Beta][i1_,k1_]\[Rho]]^2/;BesselScalar[1,i1,k1,i1,k1,\[Rho]]=!=$Failed\[And]FreeQ[b,\[Rho]]:>b BesselScalar[1,i1,k1,i1,k1,\[Rho]]},{1}];]];
ts2+=First[Timing[temp=Replace[temp,{b_. BesselJ[i1_,\[Beta][i1a_,k1_]\[Rho]]BesselJ[i2_,\[Beta][i2a_,k2_]\[Rho]]\[Rho]^a_./;BesselScalar[\[Rho]^a,i1,i1a,k1,i2,i2a,k2,\[Rho]]=!=$Failed\[And]FreeQ[b,\[Rho]]:>b BesselScalar[\[Rho]^a,i1,i1a,k1,i2,i2a,k2,\[Rho]],b_. BesselJ[i1_,\[Beta][i1a_,k1_]\[Rho]]BesselJ[i2_,\[Beta][i2a_,k2_]\[Rho]]/;BesselScalar[1,i1,i1a,k1,i2,i2a,k2,\[Rho]]=!=$Failed\[And]FreeQ[b,\[Rho]]:>b BesselScalar[1,i1,i1a,k1,i2,i2a,k2,\[Rho]]},{1}];]];
temp=(temp-Pif)/.\[Beta]->bz;
If[FreeQ[temp,\[Rho]],Return[temp],Print[temp]];
temp=Normal[Series[temp,{\[Rho],0,30}]];
Return[Integrate[temp,{\[Rho],0,1}]];
On[NIntegrate::"ploss"];
];


(* ::Text::Closed:: *)
(*\:041f\:0440\:043e\:0432\:0435\:0440\:043a\:0438*)


(* ::Input:: *)
(*Table[BesselNorm[i,j],{i,0,3},{j,0,3}]//N*)


(* ::Input:: *)
(*NIntegrate[(BesselJ[1,\[Rho] bz[0,1]]BesselJ[1,\[Rho] bz[1,1]])/\[Rho],{\[Rho],0,1}]*)


(* ::Input:: *)
(*BesselScalar[\[Rho]^-1,1,0,1,1,1,1,\[Rho]]*)


(* ::Input:: *)
(*GetHarmCoef[\!\( *)
(*\*UnderoverscriptBox[\(\[Sum]\), \(ir = 1\), \(3\)]\( *)
(*\*UnderoverscriptBox[\(\[Sum]\), \(i\[Phi] = 0\), \(3\)]*)
(*SubscriptBox[\(v\), \(ir, i\[Phi]\)] BesselJ[i\[Phi], bz[i\[Phi], ir] \[Rho]] *)
(*\*SuperscriptBox[\(E\), \(\[ImaginaryI]\ i\[Phi]\ \[Phi]\)]\)\),1,2]//Chop//Timing*)


(* ::Input:: *)
(*GetHarmCoefSymb[\!\( *)
(*\*UnderoverscriptBox[\(\[Sum]\), \(ir = 1\), \(3\)]\( *)
(*\*UnderoverscriptBox[\(\[Sum]\), \(i\[Phi] = 0\), \(3\)]*)
(*SubscriptBox[\(v\), \(ir, i\[Phi]\)] BesselJ[i\[Phi], \[Beta][i\[Phi], ir] \[Rho]] *)
(*\*SuperscriptBox[\(E\), \(\[ImaginaryI]\ i\[Phi]\ \[Phi]\)]\)\),1,2]//Chop//Timing*)


(* ::Text::Closed:: *)
(*\:0420\:0430\:0437\:043b\:043e\:0436\:0435\:043d\:0438\:0435 \:0440\:0430\:0437\:043b\:0438\:0447\:043d\:044b\:0445 \:0444\:0443\:043d\:043a\:0446\:0438\:0439 \:043f\:043e \:0431\:0430\:0437\:0438\:0441\:0443*)


(* ::Input:: *)
(*fi=FunctionInterpolation[If[r<1/2,r,-2(1-r)],{r,0,1},InterpolationOrder->1,MaxRecursion->20];*)


(* ::Input:: *)
(*fi=(1-#^2)&;*)


(* ::Input:: *)
(*fi=Function[r,r^2 (1-r)(r-1/2)];*)


(* ::Input:: *)
(*fi=Function[\[Rho],BesselJ[1,\[Rho] bz[0,1]] /\[Rho]^1 (1-\[Rho])^1 E^(\[ImaginaryI] \[Phi])];*)


(* ::Input:: *)
(*Plot[fi[r]/.\[Phi]->0,{r,0,1}];*)


(* ::Input:: *)
(*ebas=GetHarmCoef[fi[\[Rho]],0,#]&/@Range[10]*)


(* ::Input:: *)
(*ebas=GetHarmCoefSymb[fi[\[Rho]],1,#]&/@Range[10]*)


(* ::Text:: *)
(*\:041f\:0440\:043e\:0432\:0435\:0440\:043a\:0430 \:043e\:0440\:0442\:043e\:0433\:043e\:043d\:0430\:043b\:044c\:043d\:043e\:0441\:0442\:0438 \:043e\:0441\:0442\:0430\:0442\:043a\:0430*)


(* ::Input:: *)
(*firev=FunctionInterpolation[fi[r]-\!\( *)
(*\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(10\)]ebas[[i]] BesselJ[0, bz[0, i] r]\),{r,0,1}];*)


(* ::Input:: *)
(*firev=FunctionInterpolation[fi[r]-\!\( *)
(*\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(10\)]ebas[[i]] BesselJ[1, bz[1, i] r]\)/.{\[Phi]->0},{r,-0.2,1.2}];*)


(* ::Input:: *)
(*Plot[firev[r],{r,0,1}];*)


(* ::Input:: *)
(*Plot[\!\( *)
(*\*UnderoverscriptBox[\(\[Sum]\), \(i = 1\), \(10\)]ebas[[i]] BesselJ[1, bz[1, i] r]\),{r,0,1},PlotRange->All];*)


(* ::Subsubsection::Closed:: *)
(*\:0421\:0438\:0441\:0442\:0435\:043c\:0430 \:043d\:0430 \:043a\:043e\:044d\:0444\:0444\:0438\:0446\:0438\:0435\:043d\:0442\:044b \:0440\:0430\:0437\:043b\:043e\:0436\:0435\:043d\:0438\:044f \:043f\:043e \:0446\:0438\:043b\:0438\:043d\:0434\:0440\:0438\:0447\:0435\:0441\:043a\:0438\:043c \:0433\:0430\:0440\:043c\:043e\:043d\:0438\:043a\:0430\:043c*)


(* ::Text:: *)
(*\:041c\:043d\:043e\:0436\:0438\:0442\:0435\:043b\:044c \:0434\:043b\:044f \:0443\:0434\:0430\:043b\:0435\:043d\:0438\:044f \:0441\:0438\:043d\:0433\:0443\:043b\:044f\:0440\:043d\:043e\:0441\:0442\:0435\:0439 \:0432 \:0446\:0435\:043d\:0442\:0440\:0435 \:0441\:0435\:0447\:0435\:043d\:0438\:044f*)


(* ::Input:: *)
(*\[Rho]^Exponent[eqs\[Phi]r[\[Lambda],0,\[Kappa],G,Re],\[Rho]^-1]*)


(* ::Input:: *)
(*(*\:0422.\:043a. \:0443 v\[Zeta] \:043c\:0430\:043a\:0441\:0438\:043c\:0443\:043c 2 \:043f\:0440\:043e\:0438\:0437\:0432\:043e\:0434\:043d\:0430\:044f \:043f\:043e \[Rho], \:0430 \:0443 \[Psi] \:043c\:0430\:043a\:0441\:0438\:043c\:0443\:043c 4, \:0442\:043e \:0444\:0438\:043a\:0442\:0438\:0432\:043d\:044b\:0435 \:0441\:043b\:043e\:0438 - \:0443 v\[Zeta](f)=1, \:0443 \[Psi](g)=2*)*)


(* ::Text::Closed:: *)
(*\:0412\:0430\:0440\:0438\:0430\:043d\:0442 \:0438\:043d\:0442\:0435\:0433\:0440\:0438\:0440\:043e\:0432\:0430\:043d\:0438\:044f \:0432 \:043b\:043e\:0431*)


(* ::Input:: *)
(*SpectralMatrix4EigenDumb[nr_,n\[Phi]_,subst___]:=Block[{\[Rho],unk(*,systcf,cfs,v,\[Psi]c,vir,\[Rho]mul,lhs,rhs*)},*)
(*\[Rho]mul=Exponent[eqs\[Phi]r[\[Lambda],0,\[Kappa],G,Re],\[Rho]^-1];*)
(*\[Rho]mul={1,1};*)
(*vir=\[Rho]^\[Rho]mul ReplaceAll[eqs\[Phi]r[\[Lambda],\[Omega],\[Kappa],G,Re],{v\[Zeta]->Function[{\[Rho],\[Phi]},\!\( *)
(*\*UnderoverscriptBox[\(\[Sum]\), \(ir = 1\), \(nr\)]\( *)
(*\*UnderoverscriptBox[\(\[Sum]\), \(i\[Phi] = 0\), \(n\[Phi]\)]*)
(*SubscriptBox[\(v\), \(ir, i\[Phi]\)] BesselJ[i\[Phi], bz[i\[Phi], ir] \[Rho]] *)
(*\*SuperscriptBox[\(E\), \(\[ImaginaryI]\ i\[Phi]\ \[Phi]\)]\)\)],\[Psi]->Function[{\[Rho],\[Phi]},\!\( *)
(*\*UnderoverscriptBox[\(\[Sum]\), \(ir = 1\), \(nr\)]\( *)
(*\*UnderoverscriptBox[\(\[Sum]\), \(i\[Phi] = 0\), \(n\[Phi]\)]*)
(*SubscriptBox[\(\[Psi]c\), \(ir, i\[Phi]\)] BesselJ[i\[Phi], bz[i\[Phi], ir] \[Rho]] *)
(*\*SuperscriptBox[\(E\), \(\[ImaginaryI]\ i\[Phi]\ \[Phi]\)]\)\)],subst}];*)
(*unk=Flatten[Table[{Subscript[v, ir,i\[Phi]],Subscript[\[Psi]c, ir,i\[Phi]]},{ir,1,nr},{i\[Phi],0,n\[Phi]}]];*)
(*systcf=Outer[D[#1,#2]&,vir,unk];*)
(*cfs=Map[Flatten[Table[GetHarmCoef[#,i\[Phi],ir],{ir,nr},{i\[Phi],0,n\[Phi]}]]&,systcf,{2}];*)
(*cfs=Flatten/@Transpose[cfs];*)
(*lhs=-Coefficient[cfs,\[Lambda],0];*)
(*rhs=Coefficient[cfs,\[Lambda],1];*)
(*Return[{lhs,rhs}];*)
(*];*)


(* ::Text::Closed:: *)
(*\:0412\:0430\:0440\:0438\:0430\:043d\:0442 \:0441 \:0438\:043d\:0442\:0435\:0433\:0440\:0438\:0440\:043e\:0432\:0430\:043d\:0438\:0435\:043c \:043f\:043e\:0441\:043b\:0435*)


SpectralMatrix4Eigen[nr_,n\[Phi]_,subst___]:=Block[{\[Rho],(*unk,systcf,cfs,v,\[Psi]c,vir,\[Rho]mul,lhs,rhs*)},
\[Rho]mul=Exponent[eqs\[Phi]r[\[Lambda],0,\[Kappa],G,Re],\[Rho]^-1];
\[Rho]mul={1,1};
tsoth+=First[Timing[vir=\[Rho]^\[Rho]mul ReplaceAll[eqs\[Phi]r[\[Lambda],\[Omega],\[Kappa],G,Re],{v\[Zeta]->Function[{\[Rho],\[Phi]},\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(ir = 1\), \(nr\)]\(
\*UnderoverscriptBox[\(\[Sum]\), \(i\[Phi] = 0\), \(n\[Phi]\)]
SubscriptBox[\(v\), \(ir, i\[Phi]\)] BesselJ[i\[Phi], \[Beta][i\[Phi], ir] \[Rho]] 
\*SuperscriptBox[\(E\), \(\[ImaginaryI]\ i\[Phi]\ \[Phi]\)]\)\)],\[Psi]->Function[{\[Rho],\[Phi]},\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(ir = 1\), \(nr\)]\(
\*UnderoverscriptBox[\(\[Sum]\), \(i\[Phi] = 0\), \(n\[Phi]\)]
SubscriptBox[\(\[Psi]c\), \(ir, i\[Phi]\)] BesselJ[i\[Phi], \[Beta][i\[Phi], ir] \[Rho]] 
\*SuperscriptBox[\(E\), \(\[ImaginaryI]\ i\[Phi]\ \[Phi]\)]\)\)],subst}];
unk=Flatten[Table[{Subscript[v, ir,i\[Phi]],Subscript[\[Psi]c, ir,i\[Phi]]},{ir,1,nr},{i\[Phi],0,n\[Phi]}]];
systcf=Outer[D[#1,#2]&,vir,unk];]];
cfs=Map[Flatten[Table[GetHarmCoefSymb[#,i\[Phi],ir],{ir,nr},{i\[Phi],0,n\[Phi]}]]&,systcf,{2}];
tslast+=First[Timing[cfs=Flatten/@Transpose[cfs];
lhs=-Coefficient[cfs,\[Lambda],0];
rhs=Coefficient[cfs,\[Lambda],1];]];
Return[{lhs,rhs}];
];


(* ::Text::Closed:: *)
(*\:0420\:0443\:0447\:043d\:044b\:0435 \:043f\:0440\:043e\:0431\:044b*)


(* ::Input:: *)
(*With[{nr=1,n\[Phi]=1,subst=Sequence[]},*)
(*\[Rho]mul=Exponent[eqs\[Phi]r[\[Lambda],0,\[Kappa],G,Re],\[Rho]^-1];*)
(*\[Rho]mul={1,1};*)
(*vir=\[Rho]^\[Rho]mul ReplaceAll[eqs\[Phi]r[\[Lambda],\[Omega],\[Kappa],G,Re],{v\[Zeta]->Function[{\[Rho],\[Phi]},\!\( *)
(*\*UnderoverscriptBox[\(\[Sum]\), \(ir = 1\), \(nr\)]\( *)
(*\*UnderoverscriptBox[\(\[Sum]\), \(i\[Phi] = 0\), \(n\[Phi]\)]*)
(*SubscriptBox[\(v\), \(ir, i\[Phi]\)] BesselJ[i\[Phi], \[Beta][i\[Phi], ir] \[Rho]] *)
(*\*SuperscriptBox[\(E\), \(\[ImaginaryI]\ i\[Phi]\ \[Phi]\)]\)\)],\[Psi]->Function[{\[Rho],\[Phi]},\!\( *)
(*\*UnderoverscriptBox[\(\[Sum]\), \(ir = 1\), \(nr\)]\( *)
(*\*UnderoverscriptBox[\(\[Sum]\), \(i\[Phi] = 0\), \(n\[Phi]\)]*)
(*SubscriptBox[\(\[Psi]c\), \(ir, i\[Phi]\)] BesselJ[i\[Phi], \[Beta][i\[Phi], ir] \[Rho]] *)
(*\*SuperscriptBox[\(E\), \(\[ImaginaryI]\ i\[Phi]\ \[Phi]\)]\)\)],subst}];*)
(*unk=Flatten[Table[{Subscript[v, ir,i\[Phi]],Subscript[\[Psi]c, ir,i\[Phi]]},{ir,1,nr},{i\[Phi],0,n\[Phi]}]];*)
(*systcf=Outer[D[#1,#2]&,vir,unk];*)
(*cfs=Map[Flatten[Table[GetHarmCoefSymb[#,i\[Phi],ir],{ir,nr},{i\[Phi],0,n\[Phi]}]]&,systcf,{2}];*)
(*cfs=Flatten/@Transpose[cfs];*)
(*lhs=-Coefficient[cfs,\[Lambda],1];*)
(*rhs=Coefficient[cfs,\[Lambda],0];*)
(*]*)


(* ::Input:: *)
(*Timing[GetHarmCoef[#,1,1]&/@Flatten[systcf/.\[Beta]->bz]]*)


(* ::Input:: *)
(*Timing[GetHarmCoefSymb[#,1,1]&/@Flatten[systcf]]*)


(* ::Input:: *)
(*cfs1=Map[Flatten[Table[GetHarmCoef[#,i\[Phi],ir],{ir,1},{i\[Phi],0,1}]]&,systcf/.\[Beta]->bz,{2}];*)


(* ::Input:: *)
(*cfs2=Map[Flatten[Table[GetHarmCoefSymb[#,i\[Phi],ir],{ir,1},{i\[Phi],0,1}]]&,systcf,{2}];*)


(* ::Input:: *)
(*%124-%123//Chop*)


(* ::Input:: *)
(*cfs1-cfs2//Chop*)


(* ::Text::Closed:: *)
(*\:0421\:0440\:0430\:0432\:043d\:0435\:043d\:0438\:0435 \:0434\:0432\:0443\:0445 \:0441\:043f\:043e\:0441\:043e\:0431\:043e\:0432*)


(* ::Input:: *)
(*With[{nr=2,n\[Phi]=2},Map[Flatten[Table[GetHarmCoef[#,i\[Phi],ir],{ir,nr},{i\[Phi],0,n\[Phi]}]]&,systcf0,{2}]-Map[Flatten[Table[GetHarmCoefSymb[#,i\[Phi],ir],{ir,nr},{i\[Phi],0,n\[Phi]}]]&,systcf,{2}]]//Chop*)


(* ::Input:: *)
(*rhs/.{G->4,Re->1,\[Omega]->0,\[Epsilon]->0,\[Kappa]->0.1}//TableForm*)


(* ::Input:: *)
(*Timing[mat=SpectralMatrix4Eigen[5,5];]*)


(* ::Input:: *)
(*Timing[mat1=SpectralMatrix4Eigen1[5,5];]*)


(* ::Input:: *)
(*{ts\[Phi],ts1,ts2,tsoth,tslast}*)


(* ::Input:: *)
(*Max[Abs[Flatten[mat1-mat//Chop]]]*)


(* ::Section:: *)
(*\:0418\:0441\:0441\:043b\:0435\:0434\:043e\:0432\:0430\:043d\:0438\:0435 \:0432\:043e\:0437\:043c\:0443\:0449\:0435\:043d\:0438\:0439*)


(* ::Subsection:: *)
(*\:0424\:0443\:043d\:043a\:0446\:0438\:0438 \:043d\:0430\:0445\:043e\:0436\:0434\:0435\:043d\:0438\:044f \:0438\:043d\:043a\:0440\:0435\:043c\:0435\:043d\:0442\:043e\:0432*)


(* ::Subsubsection::Closed:: *)
(*\:041f\:043e\:043b\:0443\:0447\:0435\:043d\:0438\:0435 \:0441.\:0437. \:0438 \:0441.\:0432. \:0441 \:043f\:043e\:043c\:043e\:0449\:044c\:044e Eigen...[Inverse[a].m] (\:043c\:0435\:043d\:0435\:0435 \:0443\:0441\:0442\:043e\:0439\:0447\:0438\:0432\:043e)*)


(* ::Input:: *)
(*GetIncrements[n_,m_,k1_,R1_]:=Eigenvalues[Inverse[Last[#]].First[#]&[N[FiniteMatrix4Eigen[n,m,k->k1,R->R1]]]];*)


(* ::Input:: *)
(*GetEigenWave[n1_,m_,k1_,R1_,mode_:1]:=Block[{eigval,eigvec,nom,syst},syst=Inverse[Last[#]].First[#]&[N[FiniteMatrix4Eigen[n1,m,k->k1,R->R1]]];*)
(*{eigval,eigvec}=Select[Transpose[Eigensystem[syst]],NumericQ[First[#]]&]//Transpose;*)
(*nom=Flatten[Position[eigval,Sort[eigval,Re[#1]>Re[#2]&][[mode]]]]//First;*)
(*Print["Main eigen value is ",eigval[[nom]]];*)
(*Return[eigvec[[nom]]];];*)


(* ::Subsubsection::Closed:: *)
(*\:041f\:043e\:043b\:0443\:0447\:0435\:043d\:0438\:0435 \:0441.\:0437. \:0438 \:0441.\:0432. \:0441 \:043f\:043e\:043c\:043e\:0449\:044c\:044e Eigen...[{m,a}]*)


GetIncrementsM[mat_,subst_List:{}]:=Select[Eigenvalues[mat/.subst],NumericQ];


GetEigenWaveM[syst_,nr_,n\[Phi]_,subst_List,mode_:1]:=Block[{eigval,eigvec,nom,cfs},
{eigval,eigvec}=Select[Transpose[Eigensystem[syst/.subst]],NumericQ[First[#]]&]//Transpose;
nom=Flatten[Position[eigval,Sort[eigval,Re[#1]>Re[#2]&][[mode]]]]//First;
Print["Main eigen value is ",eigval[[nom]]];
cfs=Partition[#,n\[Phi]+1]&/@Partition[eigvec[[nom]],Length[eigvec[[nom]]]/2];
Return[\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(ir = 1\), \(nr\)]\(
\*UnderoverscriptBox[\(\[Sum]\), \(i\[Phi] = 0\), \(n\[Phi]\)]cfs[[#, ir, i\[Phi] + 1]] BesselJ[i\[Phi], bz[i\[Phi], ir] \[Rho]] 
\*SuperscriptBox[\(E\), \(\[ImaginaryI]\ i\[Phi]\ \[Phi]\)]\)\)&/@{1,2}]
];


GetIncrements[nr_,n\[Phi]_,\[Kappa]1_,R1_,subst___]:=Select[Eigenvalues[N[SpectralMatrix4Eigen[nr,n\[Phi],\[Kappa]->\[Kappa]1,Re->R1,subst,\[Omega]->0,\[Epsilon]->0,G->4]]],NumericQ];


GetEigenWave[n1_,m_,k1_,R1_,mode_:1]:=Block[{eigval,eigvec,nom,syst,cfs},syst=N[SpectralMatrix4Eigen[n1,m,k->k1,Re->R1,\[Omega]->0,\[Epsilon]->0,G->4]];
{eigval,eigvec}=Select[Transpose[Eigensystem[syst]],NumericQ[First[#]]&]//Transpose;
nom=Flatten[Position[eigval,Sort[eigval,Re[#1]>Re[#2]&][[mode]]]]//First;
Print["Main eigen value is ",eigval[[nom]]];
cfs=Partition[#,n\[Phi]+1]&/@Partition[eigvec[[nom]],Length[eigvec[[nom]]]/2];
Return[\!\(
\*UnderoverscriptBox[\(\[Sum]\), \(ir = 1\), \(nr\)]\(
\*UnderoverscriptBox[\(\[Sum]\), \(i\[Phi] = 0\), \(n\[Phi]\)]cfs[[#, ir, i\[Phi] + 1]] BesselJ[i\[Phi], bz[i\[Phi], ir] \[Rho]] 
\*SuperscriptBox[\(E\), \(\[ImaginaryI]\ i\[Phi]\ \[Phi]\)]\)\)&/@{1,2}]
];


GetMainIncrement[mat_,k1_,R1_,num_:1]:=(*GetMainIncrement[n,k1,R1,num]=*)(Print[{num,k1,R1}];Take[Sort[Re/@GetIncrementsM[mat,{\[Kappa]->k1,Re->R1,G->4,\[Omega]->0,\[Epsilon]->0}]],{-num}]//First);


(* ::Subsubsection::Closed:: *)
(*\:041f\:0440\:043e\:0432\:0435\:0440\:043a\:0438*)


(* ::Input:: *)
(*Take[Sort[GetIncrements[20,0,1,100],Re[#1]>Re[#2]&],10]*)


(* ::Input:: *)
(*GetMainIncrement[100,0,1,100,2]*)


(* ::Input:: *)
(*(*\:041e\:0442\:043a\:043b\:043e\:043d\:0435\:043d\:0438\:044f \:0432 \:043e\:043f\:0440\:0435\:0434\:0435\:043b\:0438\:0442\:0435\:043b\:0435 \:043f\:043e\:0441\:043b\:0435 \:043f\:043e\:0434\:0441\:0442\:0430\:043d\:043e\:0432\:043a\:0438 \:0441\:043e\:0431\:0441\:0442\:0432\:0435\:043d\:043d\:043e\:0433\:043e \:0437\:043d\:0430\:0447\:0435\:043d\:0438\:044f*)
(*With[{n2=3,m=0,k2=1,R2=100,mod=1},Det[SetPrecision[First[#]-Sort[GetIncrements[n2,m,k2,R2],Re[#1]>Re[#2]&][[mod]]Last[#],1000]]&[SetPrecision[FiniteMatrix4Eigen[n2,m,k->k2,R->R2],1000]]]*)*)


(* ::Input:: *)
(*(*\:041e\:0442\:043a\:043b\:043e\:043d\:0435\:043d\:0438\:044f \:0432 \:0432\:0435\:043a\:0442\:043e\:0440\:0435 \:043f\:043e\:0441\:043b\:0435 \:043f\:043e\:0434\:0441\:0442\:0430\:043d\:043e\:0432\:043a\:0438 \:0441\:043e\:0431\:0441\:0442\:0432\:0435\:043d\:043d\:044b\:0445 \:0437\:043d\:0430\:0447\:0435\:043d\:0438\:0439 \:0438 \:0432\:0435\:043a\:0442\:043e\:0440\:043e\:0432*)*)
(*With[{n2=300,m=0,k2=1,R2=1000,mod=2},(First[#]-Sort[GetIncrements[n2,m,k2,R2],Re[#1]>Re[#2]&][[mod]]Last[#]).GetEigenWave[n2,m,k2,R2,mod]&[FiniteMatrix4Eigen[n2,m,k->k2,R->R2]]]//Abs//PrintRange;*)


(* ::Input:: *)
(*Timing[mat=SpectralMatrix4Eigen[5,5];]*)


(* ::Input:: *)
(*SetWorkDir[];*)


(* ::Input:: *)
(*DumpSave["spectral_matrix5x5k2G2.mx",mat];*)


(* ::Input:: *)
(*<<"spectral_matrix5x5k2G2.mx"*)


(* ::Input:: *)
(*<<"spectral_matrix5x5k2.mx"*)


(* ::Input:: *)
(*<<"spectral_matrix5x5.mx"*)


(* ::Input:: *)
(*PrintRange[Re[GetIncrementsM[mat,{\[Kappa]->0.0,\[Omega]->0,G->4,\[Epsilon]->0,Re->1000}]]]*)


(* ::Input:: *)
(*mat1=mat/.{\[Kappa]->1,\[Omega]->0,G->4,\[Epsilon]->0,Re->10};*)


(* ::Input:: *)
(*Re/@GetIncrementsM[mat,{\[Kappa]->0.08,\[Omega]->-1,G->4,\[Epsilon]->0,Re->100}]//Sort*)


(* ::Subsection:: *)
(*\:0418\:0441\:0441\:043b\:0435\:0434\:043e\:0432\:0430\:043d\:0438\:0435 \:0433\:043b\:0430\:0432\:043d\:044b\:0445 \:0433\:0430\:0440\:043c\:043e\:043d\:0438\:043a*)


(* ::Input:: *)
(*Short[ew=GetEigenWaveM[mat,5,5,{\[Kappa]->0.08,\[Omega]->-1,G->4,\[Epsilon]->0,Re->100},1]//Chop,10]*)


(* ::Input:: *)
(*Simplify[Map[Im,ew,{2}]//.{Im[a_ b_]->Re[a]Im[b]+Im[a]Re[b]},\[Phi]\[Element]Reals\[And]\[Rho]>0]*)


(* ::Input:: *)
(*ew/.{\[Rho]->0.2,\[Phi]->0}*)


(* ::Input:: *)
(*NumMode[expr_]:=Block[{ex=Chop[expr,10^-5],modes},modes=Union[Extract[ex,Position[ex,Complex[0,n_Integer] \[Phi]]]]/(\[ImaginaryI] \[Phi]);*)
(*Return[If[Length[modes]==0,{0},modes]];*)
(*];*)


(* ::Input:: *)
(*NumMode/@ew*)


(* ::Subsubsection::Closed:: *)
(*\:0421\:0445\:043e\:0434\:0438\:043c\:043e\:0441\:0442\:044c*)


(* ::Input:: *)
(*linctor1=Table[Sort[GetIncrements[n,3,0.2,1],Re[#1]>Re[#2]&]//Chop,{n,1,10}];*)


(* ::Input:: *)
(*linctor2=Table[Sort[GetIncrements[2,n,0.2,1],Re[#1]>Re[#2]&]//Chop,{n,1,10}];*)


(* ::Subsubsection::Closed:: *)
(*\:0412 \:0437\:0430\:0432\:0438\:0441\:0438\:043c\:043e\:0441\:0442\:0438 \:043e\:0442 nfi*)


(* ::Input:: *)
(*PrintRange[Re[#[[3]]]&/@linctor2];*)


(* ::Input:: *)
(*PrintRange[#[[1]]&/@Log[Abs[(#-Take[linctor1[[-1]],Length[#]])&/@linctor1]]];*)


(* ::Subsubsection::Closed:: *)
(*\:0412 \:0437\:0430\:0432\:0438\:0441\:0438\:043c\:043e\:0441\:0442\:0438 \:043e\:0442 nr*)


(* ::Input:: *)
(*PrintRange[Re[#[[4]]]&/@linctor1];*)


(* ::Input:: *)
(*PrintRange[#[[7]]&/@Log[Abs[(#-Take[linctor1[[-1]],Length[#]])&/@linctor1]]];*)


(* ::Input:: *)
(*Flatten[Take[Last[linctor1],50][[#]]&/@Position[nm,1]]*)


(* ::Subsubsection:: *)
(*\:0412\:0438\:0437\:0443\:0430\:043b\:0438\:0437\:0430\:0446\:0438\:044f*)


(* ::Text::Closed:: *)
(*\:041d\:043e\:043c\:0435\:0440\:0430 \:043c\:043e\:0434*)


(* ::Input:: *)
(*nm=NumMode[GetEigenWaveM[mat,5,5,{\[Kappa]->0,\[Omega]->0,G->4,\[Epsilon]->0,Re->1},#]]&/@Range[50]*)


(* ::Output:: *)
(*{2,2,0,0,1,1,1,1,2,2,0,3,3,2,2,0,1,1,4,4,3,3,5,5,4,4,1,1,2,2,0,6,6,5,5,7,7,3,3,6,6,2,2,0,8,8,7,7,1,1}*)


(* ::Input:: *)
(*{v\[Zeta]si,\[Psi]si}=Function[{\[Rho],\[Phi]},#]&/@Simplify[Map[Re,ew,{3}],\[Phi]\[Element]Reals\[And]\[Rho]>0];*)


(* ::Text::Closed:: *)
(*\:0417\:0430\:0432\:0438\:0441\:0438\:043c\:043e\:0441\:0442\:044c \:043e\:0442 \:0440\:0430\:0434\:0438\:0443\:0441\:0430*)


(* ::Input:: *)
(*Plot[v\[Zeta]si[r,0.4],{r,0,1},PlotRange->All]*)
(*Plot[\[Psi]si[r,0.4],{r,0,1},PlotRange->All]*)


(* ::Text::Closed:: *)
(*\:0417\:0430\:0432\:0438\:0441\:0438\:043c\:043e\:0441\:0442\:044c \:043e\:0442 \:0443\:0433\:043b\:0430*)


(* ::Input:: *)
(*Plot[v\[Zeta]si[1/4,\[Phi]],{\[Phi],0,2\[Pi]}]*)
(*Plot[\[Psi]si[1/4,\[Phi]],{\[Phi],0,2\[Pi]}]*)


(* ::Text:: *)
(*\:0414\:0432\:0443\:043c\:0435\:0440\:043d\:044b\:0435 \:043a\:0430\:0440\:0442\:0438\:043d\:043a\:0438 - Density*)


(* ::Input:: *)
(*g1=PolarDensityPlot[v\[Zeta]si[r,f],{r,0,1},{f},PlotPoints->30]*)
(*g2=PolarDensityPlot[\[Psi]si[r,f],{r,0,1},{f},PlotPoints->30]*)


(* ::Text:: *)
(*\:0414\:0432\:0443\:043c\:0435\:0440\:043d\:044b\:0435 \:043a\:0430\:0440\:0442\:0438\:043d\:043a\:0438 - Contour*)


(* ::Input:: *)
(*g3=PolarContourPlot[v\[Zeta]si[r,f],{r,0,1},{f},PlotPoints->50,Contours->30]*)
(*g4=PolarContourPlot[\[Psi]si[r,f],{r,0,1},{f},PlotPoints->50,Contours->30]*)


(* ::Subsection::Closed:: *)
(*\:0421\:043f\:0435\:043a\:0442\:0440 \:043d\:0430 \:043a\:043e\:043c\:043f\:043b\:0435\:043a\:0441\:043d\:043e\:0439 \:043f\:043b\:043e\:0441\:043a\:043e\:0441\:0442\:0438*)


(* ::Input:: *)
(*Manipulate[incrs=Sort[GetIncrementsM[mat,{\[Kappa]->\[Kappa]1,\[Omega]->\[Omega]1,G->4,\[Epsilon]->0,Re->Re1}]//N,Re[#1]>Re[#2]&];*)
(*(*Print[Max[Re/@incrs]];*)*)
(*Show[Graphics[{PointSize[0.04],Point[{Re[#],Im[#]}]&/@incrs}],Axes->True,PlotRange->{Automatic,Automatic}]*)
(*,{\[Kappa]1,0,1},{Re1,1,1000},{{\[Omega]1,0},-2,2}]*)


(* ::Subsection::Closed:: *)
(*\:0417\:0430\:0432\:0438\:0441\:0438\:043c\:043e\:0441\:0442\:044c \:043e\:0442 Re*)


(* ::Input:: *)
(*maxLogRe=2;*)


(* ::Input:: *)
(*Monitor[lincRe=Table[GetIncrementsM[mat,{\[Kappa]->0.5,\[Omega]->0,G->4,\[Epsilon]->0,Re->10^logRe}],{logRe,0,maxLogRe,0.1}];,logRe]*)


(* ::Input:: *)
(*PrintRange[Transpose[{Range[0,maxLogRe,0.1],Log[Abs[Transpose[lincRe][[-1]]]]}]//Re]*)


(* ::Input:: *)
(*ListPlot[Flatten[Transpose[{Range[0,maxLogRe,0.1],#}&/@Transpose[Log[Abs[Re[lincRe]]]],{1,3,2}],1],PlotRange->All]*)


(* ::Subsubsection::Closed:: *)
(*\:0418\:043d\:043a\:0440\:0435\:043c\:0435\:043d\:0442\:044b Log[10, -incr] \:043e\:0442 Log[10, Re] *)


(* ::Text:: *)
(*\[Kappa] = 0.5*)


(* ::Input:: *)
(*Show[Graphics[{{}, {Hue[0.67, 0.6, 0.6], Point[CompressedData["*)
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(*"]]}, {}}, AspectRatio -> GoldenRatio^(-1), Axes -> True, AxesOrigin -> {0, 0}, PlotRange -> {All, All}, PlotRangeClipping -> True, PlotRangePadding -> {Automatic, Automatic}],AxesLabel->{"lg Re","-lg(-\[Lambda])"},TextStyle->{FontSize->14}]*)


(* ::Text:: *)
(*\[Kappa] = 0.1*)


(* ::Text:: *)
(*\[Kappa] = 0.01*)


(* ::Text:: *)
(*\[Kappa] = 0.001*)


(* ::Text:: *)
(*\[Kappa] = 0.0*)


(* ::Subsubsection::Closed:: *)
(*\:041f\:043e\:0434\:0431\:043e\:0440 \:043f\:0430\:0440\:0430\:043c\:0435\:0442\:0440\:043e\:0432 \:044d\:043a\:0441\:043f\:043e\:043d\:0435\:043d\:0446\:0438\:0430\:043b\:044c\:043d\:043e\:0433\:043e \:0437\:0430\:0442\:0443\:0445\:0430\:043d\:0438\:044f*)


(* ::Input:: *)
(*linc=Table[{R,GetMainIncrement[100,0,1,R,2]},{R,1,20001,100}];*)


(* ::Input:: *)
(*Timing[linc=Table[{n,(GetMainIncrement[n,0,1,1000,2])},{n,10,250,10}];]*)


(* ::Input:: *)
(*gr=PrintRange[Last/@linc];*)


(* ::Input:: *)
(*If[!NumericQ[E],Remove[E]];*)
(*cutout=6;*)
(*ltest=Last/@Drop[linc,cutout];*)
(*{lna\[Lambda],\[Lambda]}=CoefficientList[Fit[Log[-dif[ltest]],{1,x},x],x];*)
(*a=-E^lna\[Lambda]/\[Lambda];Print[{a,\[Lambda]}];*)


(* ::Input:: *)
(*ListPlot[ltest-Table[a E^(\[Lambda] x),{x,1,Length[ltest]}]];*)


(* ::Subsection:: *)
(*\:0417\:0430\:0432\:0438\:0441\:0438\:043c\:043e\:0441\:0442\:044c \:043e\:0442 \:0442\:043e\:0440\:043e\:0438\:0434\:0430\:043b\:044c\:043d\:043e\:0441\:0442\:0438*)


(* ::Input:: *)
(*linc\[Kappa]=Table[GetIncrementsM[mat,{\[Kappa]->kval,\[Omega]->0,G->4,\[Epsilon]->0,Re->1}],{kval,0,1,0.01}];*)


(* ::Input:: *)
(*PrintRange[Transpose[{Range[0,1,0.01],Transpose[linc\[Kappa]][[1]]}]//Re]*)


(* ::Input:: *)
(*Quadratic[l_]:=Block[{f,tmp},*)
(*f=Fit[Chop[l],{1,k,k^2},k];*)
(*tmp=Select[k/.Solve[f==0,k],(#\[Element]Reals\[And]0<=#<1)&];*)
(*Return[If[Length[tmp]>0,{Coefficient[f,k^2],tmp},Coefficient[f,k^2]]]*)
(*]*)


(* ::Input:: *)
(*ListPlot[Flatten[Transpose[{Range[0,0.1,0.01],#}&/@Transpose[Re[linc\[Kappa]]],{1,3,2}],1],PlotRange->All]*)


(* ::Input:: *)
(*Timing[GetIncrementsM[mat,{\[Kappa]->0,\[Omega]->0,G->4,\[Epsilon]->0,Re->1000}];]*)


(* ::Input:: *)
(*ProgressIndicator[Dynamic[k1],{0,1}]*)


(* ::Subsubsection:: *)
(*\[Omega] = 0, G=4*)


(* ::Text::Closed:: *)
(*Re=1*)


(* ::Input:: *)
(*\[Kappa]max=1;d\[Kappa]=0.01;*)


(* ::Input:: *)
(*incsRe1=Monitor[Table[Take[Sort[Re/@GetIncrementsM[mat,{\[Kappa]->k1,Re->1,G->4,\[Omega]->0,\[Epsilon]->0}]],-10],{k1,0,\[Kappa]max,d\[Kappa]}],k1];*)


(* ::Input:: *)
(*PrintRange[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],Last/@incsRe1}]]*)


(* ::Input:: *)
(*ListPlot[Flatten[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}&/@Transpose[Re[incsRe1]],{1,3,2}],1],PlotRange->Automatic]*)


(* ::Input:: *)
(*Reverse[Quadratic/@(Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}]&/@Transpose[incsRe1])]*)


(* ::Text::Closed:: *)
(*Re=10*)


(* ::Input:: *)
(*\[Kappa]max=1;d\[Kappa]=0.01;*)


(* ::Input:: *)
(*incsRe10=Monitor[Table[Take[Sort[Re/@GetIncrementsM[mat,{\[Kappa]->k1,Re->10,G->4,\[Omega]->0,\[Epsilon]->0}]],-10],{k1,0,\[Kappa]max,d\[Kappa]}],k1];*)


(* ::Input:: *)
(*PrintRange[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],Last/@incsRe10}]]*)


(* ::Input:: *)
(*ListPlot[Flatten[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}&/@Transpose[Re[incsRe10]],{1,3,2}],1],PlotRange->Automatic]*)


(* ::Input:: *)
(*Reverse[Quadratic/@(Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}]&/@Transpose[incsRe10])]*)


(* ::Text::Closed:: *)
(*Re=100*)


(* ::Input:: *)
(*\[Kappa]max=0.04;d\[Kappa]=0.001;*)


(* ::Input:: *)
(*incsRe100=Monitor[Table[Take[Sort[Re/@GetIncrementsM[mat,{\[Kappa]->k1,Re->100,G->4,\[Omega]->0,\[Epsilon]->0}]],-10],{k1,0,\[Kappa]max,d\[Kappa]}],k1];*)


(* ::Input:: *)
(*PrintRange[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#[[-1]]&/@incsRe100}]]*)


(* ::Input:: *)
(*ListPlot[Flatten[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}&/@Transpose[Re[incsRe100]],{1,3,2}],1],PlotRange->Automatic]*)


(* ::Input:: *)
(*Reverse[Quadratic/@(Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}]&/@Transpose[incsRe100])]*)


(* ::Text::Closed:: *)
(*Re=1000*)


(* ::Input:: *)
(*\[Kappa]max=0.0004485124679;d\[Kappa]=0.00001;*)


(* ::Input:: *)
(*incsRe1000=Monitor[Table[Take[Sort[Re/@GetIncrementsM[mat,{\[Kappa]->k1,Re->1000,G->4,\[Omega]->0,\[Epsilon]->0}]],-10],{k1,0,\[Kappa]max,d\[Kappa]}],k1];*)


(* ::Input:: *)
(*PrintRange[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],Last/@incsRe1000}]]*)


(* ::Input:: *)
(*ListPlot[Flatten[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}&/@Transpose[Re[incsRe1000]],{1,3,2}],1],PlotRange->Automatic]*)


(* ::Input:: *)
(*Reverse[Quadratic/@(Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}]&/@Transpose[incsRe1000])]*)


(* ::Text::Closed:: *)
(*Re=10000*)


(* ::Input:: *)
(*\[Kappa]max=4.48*^-6;d\[Kappa]=1.*^-7;*)


(* ::Input:: *)
(*incsRe10000=Monitor[Table[Take[Sort[Re/@GetIncrementsM[mat,{\[Kappa]->k1,Re->10000,G->4,\[Omega]->0,\[Epsilon]->0}]],-10],{k1,0,\[Kappa]max,d\[Kappa]}],k1];*)


(* ::Input:: *)
(*PrintRange[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],Last/@incsRe10000}]]*)


(* ::Input:: *)
(*ListPlot[Flatten[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}&/@Transpose[Re[incsRe10000]],{1,3,2}],1],PlotRange->Automatic]*)


(* ::Input:: *)
(*Reverse[Quadratic/@(Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}]&/@Transpose[incsRe10000])]*)


(* ::Subsubsection:: *)
(*\[Omega] = -1, G=4*)


(* ::Text::Closed:: *)
(*Re=1*)


(* ::Input:: *)
(*\[Kappa]max=1;d\[Kappa]=0.01;*)


(* ::Input:: *)
(*incsRe1=Monitor[Table[Take[Sort[Re/@GetIncrementsM[mat,{\[Kappa]->k1,Re->1,G->4,\[Omega]->-1,\[Epsilon]->0}]],-10],{k1,0,\[Kappa]max,d\[Kappa]}],k1];*)


(* ::Input:: *)
(*PrintRange[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],Last/@incsRe1}]]*)


(* ::Input:: *)
(*ListPlot[Flatten[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}&/@Transpose[Re[incsRe1]],{1,3,2}],1],PlotRange->Automatic]*)


(* ::Input:: *)
(*Reverse[Quadratic/@(Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}]&/@Transpose[incsRe1])]*)


(* ::Text::Closed:: *)
(*Re=10*)


(* ::Input:: *)
(*\[Kappa]max=1;d\[Kappa]=0.01;*)


(* ::Input:: *)
(*incsRe10=Monitor[Table[Take[Sort[Re/@GetIncrementsM[mat,{\[Kappa]->k1,Re->10,G->4,\[Omega]->-1,\[Epsilon]->0}]],-10],{k1,0,\[Kappa]max,d\[Kappa]}],k1];*)


(* ::Input:: *)
(*PrintRange[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],Last/@incsRe10}]]*)


(* ::Input:: *)
(*ListPlot[Flatten[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}&/@Transpose[Re[incsRe10]],{1,3,2}],1],PlotRange->Automatic]*)


(* ::Input:: *)
(*Reverse[Quadratic/@(Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}]&/@Transpose[incsRe10])]*)


(* ::Text:: *)
(*Re=100*)


(* ::Input:: *)
(*\[Kappa]max=0.09;d\[Kappa]=0.001;*)


(* ::Input:: *)
(*incsRe100=Monitor[Table[Take[Sort[Re/@GetIncrementsM[mat,{\[Kappa]->k1,Re->100,G->4,\[Omega]->-1,\[Epsilon]->0}]],-10],{k1,0,\[Kappa]max,d\[Kappa]}],k1];*)


(* ::Input:: *)
(*PrintRange[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#[[-1]]&/@incsRe100}]]*)


(* ::Input:: *)
(*ListPlot[Flatten[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}&/@Transpose[Re[incsRe100]],{1,3,2}],1],PlotRange->Automatic]*)


(* ::Input:: *)
(*Reverse[Quadratic/@(Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}]&/@Transpose[incsRe100])]*)


(* ::Text::Closed:: *)
(*Re=1000*)


(* ::Input:: *)
(*\[Kappa]max=0.001;d\[Kappa]=0.00001;*)


(* ::Input:: *)
(*incsRe1000=Monitor[Table[Take[Sort[Re/@GetIncrementsM[mat,{\[Kappa]->k1,Re->1000,G->4,\[Omega]->-1,\[Epsilon]->0}]],-10],{k1,0,\[Kappa]max,d\[Kappa]}],k1];*)


(* ::Input:: *)
(*PrintRange[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#[[-1]]&/@incsRe1000}]]*)


(* ::Input:: *)
(*ListPlot[Flatten[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}&/@Transpose[Re[incsRe1000]],{1,3,2}],1],PlotRange->Automatic]*)


(* ::Input:: *)
(*Export["incrs.eps",Graphics[{{}, {Hue[0.67, 0.6, 0.6], Point[CompressedData["*)
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(*"]]}, {}}, AspectRatio -> GoldenRatio^(-1), Axes -> True, AxesOrigin -> {0, -0.05}, ImageSize -> {214., Automatic}, PlotRange -> {{0., 0.001}, {-0.04993471125085637, -0.005377739825551988}}, PlotRangeClipping -> True, PlotRangePadding -> {Scaled[0.02], Scaled[0.02]}],ImageResolution->100,ImageSize->500]*)


(* ::Input:: *)
(*Reverse[Quadratic/@(Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}]&/@Transpose[incsRe1000])]*)


(* ::Text::Closed:: *)
(*Re=10000*)


(* ::Input:: *)
(*\[Kappa]max=1*^-5;d\[Kappa]=1.*^-7;*)


(* ::Input:: *)
(*incsRe10000=Monitor[Table[Take[Sort[Re/@GetIncrementsM[mat,{\[Kappa]->k1,Re->10000,G->4,\[Omega]->-1,\[Epsilon]->0}]],-10],{k1,0,\[Kappa]max,d\[Kappa]}],k1];*)


(* ::Input:: *)
(*PrintRange[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],Last/@incsRe10000}]]*)


(* ::Input:: *)
(*ListPlot[Flatten[Transpose[{Range[0,\[Kappa]max,d\[Kappa]],#}&/@Transpose[Re[incsRe10000]],{1,3,2}],1],PlotRange->Automatic]*)
